Robotics Mid-Term Project

2-Link Manipulator Animation

This project simulates a 2-link robotic manipulator following a predefined path using inverse kinematics. The manipulator is visualized using matplotlib and is controlled to follow a straight line path. The main components of this project include the manipulator (with inverse kinematics calculations), the path generator, and the plotter.

Project Structure

• constants.py: Defines constants for link lengths, step size, and the line equation.
• path_generator.py: Contains the PathGenerator class, which generates reachable points along a specified line.
• manipulator.py: Contains the Manipulator class, which calculates the inverse kinematics for reaching target points.
• plotter.py: Contains the Plotter class, which visualizes the manipulator's movement along the path and plots the joint angles over time.
• main.py: Initializes and executes the main components of the project, displaying the manipulator's animation and saving the angle plots.

Setup and Usage

1. Install required dependencies:

   pip install matplotlib

2. Run the main script:

   python main.py

   This will display an animation of the manipulator following the target path and save the joint angle plots in the angle_plots folder.

Components

Note : All units are in mm

1. Path Generator

The PathGenerator class generates path points along a target line, defined as y = -x / 2 + 100. The points are spaced by STEP_SIZE and limited by the manipulator's maximum reach.

2. Manipulator

The Manipulator class uses inverse kinematics to compute the joint angles (theta1, theta2) needed to reach a target (x, y).

Inverse Kinematics Calculation

Given a target point (x, y), the joint angles are computed as follows:

1. Calculate the Distance d:

   • d is the distance from the base to the target:
     • d = sqrt(x^2 + y^2)
   • Ensure d is within reach: d must satisfy |L1 - L2| <= d <= L1 + L2.

2. Compute theta2 (Elbow Angle):

   • Using the law of cosines:
     • cos(theta2) = (d^2 - L1^2 - L2^2) / (2 * L1 * L2)
   • Then:
     • theta2 = atan2(sqrt(1 - cos(theta2)^2), cos(theta2))

3. Compute theta1 (Shoulder Angle):

   • First, calculate the angle alpha to (x, y):
     • alpha = atan2(y, x)
   • Then adjust by the angle beta:
     • beta = atan2(L2 * sin(theta2), L1 + L2 * cos(theta2))
   • Finally:
     • theta1 = alpha - beta

4. Return Angles:

   • The calculated theta1 and theta2 represent the joint angles needed to reach (x, y).

3. Plotter

The Plotter class animates the manipulator’s movement along the target path and plots the joint angles over time. It creates and displays the animation, saving angle plots in the angle_plots directory.

Example Output

Running main.py displays an animation of the manipulator following the line path and saves shoulder and elbow angle plots as PNG files.

Dependencies

• Python 3
• matplotlib for plotting and animation